Interior Angle Theorem
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Where n is the number of polygon sides.
Interior angle theorem. So in the figure below if k l then 2 8 and 3 5. The inscribed angle theorem relates the measure of an inscribed angle. 9th mathematics parallel lines in the wake of corona threat these videos have been recorded to enable students studying at home save their time.
Interior angle sum of the interior angles of a polygon n. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate. Once you can recognize and break apart the various parts of parallel lines with transversals you can use the alternate interior angles theorem to speed up your work.
An interior angle is located within the boundary of a polygon. The proof of this theorem is straightforward. The alternate interior angles theorem states that if two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent.
The exterior angle theorem is proposition 1 16 in euclid s elements which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. The alternate interior angles theorem states that when two parallel lines are cut by a transversal the resulting alternate interior angles are congruent. The consecutive interior angles theorem states that if two parallel lines are cut by a transversal then consecutive interior angles are supplementary 180 what is the alternate interior angles theorem.
Below is the proof for the polygon interior angle sum theorem. If we know the sum of all the interior angles of a regular polygon we can obtain the interior angle by dividing the sum by the number of sides. The sum of all of the interior angles can be found using the formula s n 2 180.
Polygons interior angles theorem. The consecutive interior angles theorem states that if two parallel lines are cut by a transversal then each pair of alternate interior angles is congruent. In several high school treatments of geometry the term exterior angle.
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